Evidently not. ATC was about to issue instructions to separate traffic. It was neither failed, nor was it going to fail shortly. If TCAS "thinks" late ATC intervention is a failure of ATC, then maybe its requirements are flawed.
Yes but those instructions came too late to stop the aircraft coming within 7NM of each other at the same level, on a collision course. That, by definition, is a "failure of separation". "Late ATC intervention" is a "failure of separation", involving much form filling, suspension of the individuals involved, official reports, etc. I'm coming to think your definition of "separation" is "not actually hitting each other", which is
not an industry standard!